STTC Encoder for Single Antenna WAVE Transceivers

ABSTRACT

An encoder in a transmitter uses space-time trellis coding. An input bitstream is multiplexed to produce in parallel a set of output bitstreams. A multiplier applies a code generating weight to each output bitstream, which are combined, mapped and transmitted by a single antenna.

RELATED APPLICATIONS

This application related to non-provisional application Ser. No.12/______ “Unified STTC Encoder for Wave Transceiver,” filed by PhilipV. Orlik et al on Jul. 15, 2009, co-filed herewith.

This application claims priority to the provisional application61/165,393 filed by Philip V. Orlik on Mar. 31, 2009, and isincorporated herein.

FIELD OF THE INVENTION

This invention relates generally to transceivers, and more particularlyto WAVE single antenna transceivers using space-time trellis codes.

BACKGROUND OF THE INVENTION

Wireless access in vehicular environments (WAVE) provides high-speedvehicle-to-vehicle, and vehicle-to-infrastructure data transmission. Thephysical (PHY) layer of a WAVE network is based on the IEEE 802.11pstandard. Currently, a WAVE transceiver has one antenna, and usesconvolutional forward error correction (FEC) coding.

To achieve spatial diversity and/or multiplexing gains,multiple-input-multiple-output (MIMO) techniques can be used, e.g.,WiMAX. It is expected that MIMO will be considered for WAVE standards.

MIMO techniques include open-loop and closed-loop spatial multiplexing,closed-loop MIMO beamforming, and open-loop space-time coding (STC). Ina dynamic WAVE networks, the estimated instantaneous channel stateinformation (CSI) can quickly change because of the velocity of thevehicles. In addition, feeding back time-varying instantaneous CSIincreases overhead. Thus, closed-loop MIMO techniques are not suitablefor WAVE networks.

For open-loop MIMO techniques, STC includes space-time block codes(STBC), and space-time trellis codes (STTC). For STBC schemes,orthogonal STBC (OSTBC) is usually adopted by commercial wirelessstandards. If the channel is invariant within an OSTBC block, then asimple symbol-level maximum likelihood (ML) detection of OSTBC canachieve full spatial diversity.

In WiMAX, OSTBC is used as an inner code serially concatenated with aconventional convolutional code. Frequency offset resulting fromimperfect frequency compensation can lead to symbol-level time-varyingfading within an OSTBC block. In this case, to avoid performancedegradation, block-level ML detection is needed to decode OSTBC so as toavoid performance degradation.

For complex modulation constellation, full-rate OSTBC only exists formultiple transmit antennas. STTC on the other hand, is a full-ratetrellis coded modulation technique specifically designed only formulti-antenna transmission. The coding and decoding complexity issimilar to traditional single-antenna trellis codes (e.g., convolutionalcodes) that have the same number of trellis states as STTC

STTC has different design criteria for different channel conditions,such as “quasi-static vs. rapid” multipath fading based on the coherencetime, and “flat vs. frequency-selective” multipath fading, based on thecoherence bandwidth.

An STTC designed for a quasi-static flat fading channel can achieve atleast the same end-to-end diversity benefit for other channelconditions, without modifications of the detection algorithm. Thus,unlike OSTBC, there exist STTC schemes which are robust tounpredictable/rapid variation of channel conditions. While most STBCschemes, e.g., OSTBC, do not provide coding gain, STTC does providecoding gain.

Conventional wireless standards, which consider single- andmulti-antenna configurations, when evolving from the single-antennaconfiguration to the multi-antenna configuration, change the codingand/or decoding modules at the transceivers. This is because thestructure and process of STC encoders and decoders have obviousdifferences from those of conventional single-antenna FEC techniques,e.g., convolutional codes, and turbo codes.

Because STTC is inherently a trellis coded modulation technique, usingdifferent modulation constellations requires that STTC encodersstructures have different structures.

Convolutional Code in IEEE 802.11p Standard

As shown in FIG. 1, a conventional 64-state convolutional encoder 100according to the IEEE 802.11p standard uses a generator polynomials,g₀=133_(oct) and g₁=171_(oct), with a code rate R_(c)=½. In the encoder,each shift register 105 is a 1-bit (binary) register. The constraintlength 102 of this code is seven. That is, the memory order is six andthe number of trellis states is 2⁶=64. The input bits 101 are encodedinto coded bits. Then, the modulator 110 takes coded bits and convertsthem into transmitted symbols. The Viterbi decoding is recommended forperforming ML coherent detection.

Higher code rates (e.g., ⅔, ¾) can be achieved by puncturing. Puncturingis a procedure for omitting some of the encoded bits in the transmitterand inserting a dummy “zero” in the convolutional decoder in place ofthe omitted bits. The puncturing patterns are prescribed in the IEEE802.11p standard. When puncturing is used, in order to reuse theoriginal decoding trellis, the calculation of the branch metrics need tobe modified appropriately.

STTC Designed for Multiple Transmit Antennas

The STTC designed for n (n≧2) transmit antennas is denoted as n-Tx STTC,at each time slot t, an n-Tx STTC encodes k=log₂ M bits into n codedMPSK/MQAM symbols c_(t)=(c_(t) ¹,c_(t) ², . . . , c_(t) ^(n)). Antenna itransmits symbol c_(t) ^(i), and n coded symbols are transmittedsimultaneously by n transmit antennas, resulting in full-ratetransmission. The energy per information bit is E_(b). Because n codedAIPSK/MQAM symbols are generated from k=log₂ M information bits, theenergy for each of the n coded symbols is E_(c)=kE_(b)/n.

ML coherent detection for STTC typically uses Viterbi decoding. Comparedwith the Viterbi decoding for one receive antenna, when there are m(m≧2) receive antennas, the branch metric is the sum of m values, eachof which is obtained by using the received signal at one of m receiveantennas to do the same calculation of branch metric as for one receiveantenna.

For STTC using PSK modulation, using the code with 64 trellis states asthe example, the encoder structure for n-Tx BPSK STTC and n-Tx QPSK STTCare shown in FIGS. 2-3, respectively. In both figures, each shiftregister is a 1-bit (binary) register. For BPSK, the values of codegenerator weight g_(w,i) ¹ (w=0, 1, . . . , 6; i=1, . . . , n) belong to{0, 1}, and the multiplier outputs are added modulo 2. For QPSK, thereare two parallel encoder branches. The values of g_(w,i) ^(u) (u=1, 2;w=0, 1, . . . , 3; i=1, . . . , n) belong to {0, 1, 2, 3}, and themultiplier outputs are added modulo 4.

For STTC using QAM modulation, a generic design for n-Tx 2^(2p)-QAM STTC(p is a positive integer) is known. A 16QAM STTC encoder is described byLiu et al., “A rank criterion for QAM space-time codes,” IEEE Trans. onInform. Theory, vol. 48, no. 12, pp. 3062-3079, December 2002.

A 16-QAM decoder is described by Wong et al., “Design of 16-QAMspace-time trellis codes for quasi-static fading channels,” Proc. of VTC2004-Spring, pp. 880-883, Can 2004.

An n-Tx BPSK/QPSK encoder is described by Vucetic et al., “Space-TimeCoding,” West Sussex, England: John Wiley Sons, 2003.

In some designs, at each time slot t, the input mapper converts k=2pserial information bits into two parallel symbol streams s_(t) ¹, s_(t)² ∈ Z₂ ^(p)={0, 1, . . . , 2^(p)−1}, so that there are always twoparallel encoder branches. Based on the symbols, the generatorcoefficients, and the state values, the encoder produce the outputs asy_(t,I) ¹, y_(t,Q) ¹, . . . , y_(t,I) ^(i), y_(t,Q) ^(i), . . . ,y_(t,I) ^(n), y_(t,Q) ^(n). The output mapper takes the encoder outputsand converts them into c_(t)=(c_(t) ¹,c_(t) ², . . . , c_(t) ^(n)),where c_(t) ^(i)=y_(t,I) ^(i)+j y_(t,Q) ^(i) for i=1, . . . , n. After atranslational mapping of c_(t) ^(i) (i=1, . . . , n) to elements in the2^(2p)-QAM constellation, each of n coded 2^(2p)-QAM symbols is sent byone of n transmit antennas. Using a code with 64 trellis states as anexample, the encoder structures for n-Tx 16QAM STTC and n-Tx 64QAM STTCare shown in FIGS. 4-5.

For the 16QAM case, each shift register is a 2-bit (quaternary)register. The values of code generator parameters g_(w,i,I) ¹, g_(w,i,Q)¹ (w=0, 1; i=1, . . . , n), g_(w,i,I) ², g_(w,i,Q) ² (w=0, 1, 2; i=1, .. . , n) belong to Z₄={0, 1, 2, 3}, and the multiplier outputs are addedmodulo 4. For the 64QAM case, each shift register is a 3-bit (octal)register, the values of g_(w,i,I) ^(u), g_(w,i,Q) ^(u) (u=1, 2; w=0, 1;i=1, . . . , n) belong to Z₈={0, 1, . . . , 7}, and the multiplieroutputs are added modulo 8.

There exist STTC schemes which are robust to unpredictable variation ofchannel conditions, V. Tarokh et al., “Space-time codes for high datarate wireless communication: performance criteria in the presence ofchannel estimation errors, mobility, and multiple paths,” IEEE Trans. onCommun., vol. 47, no. 2, pp. 199-207, February 1999.

As shown in FIG. 3, the general encoder structure for n-Tx QPSK STTConly has two parallel encoder branches. If the encoder structure forn-Tx 16QAM STTC is selected for an n-antenna transmitter using n-TxQPSK/16QAM STTC, when switching the modulation constellation betweenn-Tx QPSK STTC and n-Tx 16QAM STTC, the hardware implementation requiresextensive variations.

In addition, using n=2 as the example, it has been shown in the work byWong et al., that the error performance of 16QAM STTC in the work by V.Tarokh et al., is worse.

SUMMARY OF THE INVENTION

The embodiments of the invention use n-Tx AIPSK/MQAM STTC (n≧2) as acoded modulation constellation scheme for n-antenna WAVE transceivers.

To avoid significant change in the encoder structure of n-Tx STTC whenthe modulation constellation varies, the invention provides a unifiedn-Tx STTC encoder implementation for all of the modulationconstellations specified in IEEE 802.11p standard, including BPSK, QPSK,16QAM, and 64QAM. Thus, adaptive modulation can be enabled where themodulation constellation can be adapted to changing channel conditions.And the same encoder circuitry can be used to implement the encoder foreach modulation constellation.

For a transmitter with a single antenna, the embodiments provide apseudo-STTC that can achieve coding gain and/or time diversity gain withfull rate. In the pseudo-STTC encoder, the single-antenna transmittersends a linear combination of n coded MPSK/MQAM symbols generated froman n-Tx STTC during at each time slot.

By estimating n equivalent channel coefficients at the receiver, each ofwhich is a multiplicity of the original single-antenna channelcoefficient and a linear coefficient, the pseudo-STTC can use the samecoherent decoding procedure as for n-Tx STTC. Besides giving a goodchoice of random linear coefficients, the embodiments of the inventionalso provide a specific design for optimizing deterministic linearcoefficients.

To provide a flexible code rate, we perform duplication on the originalfull-rate pseudo-STTC. In particular, when an n-Tx STTC is used as theunderlying code, for every n coded symbols, c_(t) ¹, . . . , c_(t) ^(n),we transmit q (q≧2) different versions of linear combination using qdifferent sets of linear coefficients; this scheme is calledq-duplicated pseudo-STTC.

Compared with decoding the full-rate pseudo-STTC, the decoder ofq-duplicated pseudo-STTC only needs to do simple modifications on thecalculation of the branch metric. As for the full-rate pseudo-STTC,besides giving a good choice of random linear coefficients, we alsodesign the optimal deterministic linear coefficients by focusing on2-duplicated pseudo-STTC, which uses 2-Tx STTC as the underlying code.

To unify the codec module used for single-antenna pseudo-STTC and n-TxSTTC (n≧2), for full-rate transmissions, each antenna element of then-Tx transmitter also sends a linear combination of c_(t) ¹, . . . ,c_(t) ^(n), generated from an n-Tx STTC. This kind of multi-antennacoded transmission is equivalent to conventional n-Tx STTC when, forantenna i (i=1, . . . , n), setting the linear coefficient multipliedwith c_(t) ^(i) as 1 and all the other linear coefficients as 0. Forlower-rate transmissions, each antenna element of the n-Tx transmitteralso sends q linear combinations of c_(t) ¹, . . . , c_(t) ^(n). Forantenna i, the linear coefficients used for each of q linearly combinedtransmissions are the same and have the format of setting the linearcoefficient multiplied with c_(t) ^(i) as 1 and all the others as 0. Bydoing so, antenna i (i=1, . . . , n) actually performs q repeatedtransmissions for c_(t) ^(i). This is a result of applying ourduplication concept to conventional full-rate n-Tx STTC transmissions.

The advantages of the full-rate/duplicated pseudo-STTC techniques are asfollows.

We provide unified codec modules for both single- and multi-antennatransceivers. For either single- or multi-antenna configuration, weprovide flexible code rate via duplicated approach. For single-antennaconfiguration, when compared with the IEEE 802.11p convolutional codeand its punctured versions, under either symbol-level or much slowertime-varying flat/frequency-selective fading channels, we achieve betteror comparable error performance with the same or higher data rate andwith almost the same codec complexity. Additionally, the scheme isrobust to highly dynamic channel conditions resulting fromnon-negligible Doppler spread and delay spread as well as imperfectfrequency offset compensation. For the first time, we enablesingle-antenna transmissions to achieve coding gain with full-ratetransmission.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph of a conventional 64-state convolutional encoderprescribed in the IEEE 802.11p standard;

FIG. 2 is a graph of a conventional 64-state BPSK STTC encoder for n(n≧2) transmit antennas;

FIG. 3 is a graph of a conventional 64-state QPSK STTC encoder for n(n≧2) transmit antennas;

FIG. 4 is a graph of conventional 64-state 16QAM STTC encoder for n(n≧2) transmit antennas;

FIG. 5 is a graph of conventional 64-state 64QAM STTC encoder for n(n≧2) transmit antennas;

FIG. 6 is a graph of an unified n-Tx STTC encoder according to theinvention for all of modulation constellations including BPSK, QPSK,16QAM and 64QAM specified in the IEEE 802.11p standard;

FIG. 7 is a graph of the single-antenna full-rate pseudo-STTC schemeaccording to the invention;

FIG. 8 is a graph of the single-antenna q-duplicated (q≧2) pseudo-STTCscheme according to the invention; and

FIG. 9 is a block diagram of the functional stages at the PHY layer insingle-antenna OFDM networks.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The embodiments of our invention provide space-time trellis codes (STTC)for MIMO coding in multi-antenna WAVE networks. This is based on thefollowing two facts.

As a trellis coded modulation technique for multi-antenna transmission,the codec complexity of STTC is similar to single-antenna trellis codes,e.g., convolutional codes, which have the same number of trellis statesas STTC.

We describe an unified n-Tx STTC encoder implementation for all ofmodulation constellations specified in the IEEE 802.11p standard,including BPSK, QPSK, 16QAM, and 64QAM.

We provide a novel full-rate/duplicated pseudo-STTC techniques forsingle-antenna configuration, which provides a unified codec modules forboth single- and multi-antenna transceivers. We first describe thepseudo-STTC techniques under the context of a single-carriersingle-antenna network, and then describe the application of theproposed coding techniques to an orthogonal frequency-divisionmultiplexing (OFDM) single-antenna network, e.g., a WAVE network.

Unified STTC Encoder Implementation for BPSK, QPSK, 16QAM 64QAM

STTC is a multi-antenna trellis coded modulation technique. If themodulation constellation changes, then the implementation of aconventional n-Tx STTC encoder requires extensive changes. Thus, it isdesirable to provide an encoder structure for each considered modulationproperly and further organize an unified n-Tx STTC encoder which easilyallows switching between used modulation constellation depending on aninstantaneous channel condition.

Thus, we describe a unified n-Tx STTC encoder implementation for all ofmodulation options prescribed in the IEEE 802.11p standard by combiningportions of conventional encoders in a most unusual way.

Specifically, with the focus on n-Tx STTCs having 64 trellis states, theencoder structure is shown in FIG. 6.

We use switches to select dynamically select BPSK, QPSK, 16QAM, and64QAM modulation constellations. The selection can dynamic and based onthe instantaneous channel condition.

The encoder includes a serial to parallel (S/P) convertor 610 to convertan input stream of information bits 601 to first and second parallelbitstreams 602. The encoder includes a first branch of shift registers621 and a second branch of shift registers 622. Each branch consists ofthree shift registers, and each shift register 605 has three bits. Codegenerating weights g_(w) 611 are applied to the bits of the shiftregisters using multipliers 612 as described herein to produce a firstset of encoded symbols 648, and a second set of encoded symbols.

The output encoded symbols 648-649 of the shift registers are combined640, and an output mapper 650 maps the combined output to a plurality ofantennas 651.

In the encoder 600, only for n-Tx BPSK STTC, second switch 606 is off sothat the connection between the input data and the 1^(st) register atthe second branch of shift registers 622 is disabled. Also for the n-TxBPSK STTC, first switch 607 is on so that the line between the 3^(rd)register at the first branch of registers 621 and the 1^(st) register atthe second branch of registers 622 is connected.

For QPSK, 16QAM and 64QAM, the second switch 606 is on so that theconnection between the input data and the 1^(st) register at the secondbranch of registers 622 is enabled. The first switch 607 is off so thatthe line between the 3^(rd) register at the first branch of registers621 and the 1^(st) register at the second branch of registers 622 isconnected.

For BPSK or QPSK modulation constellation, out of the three bits in eachshift registers 605, only one of the three bits are enabled.

For 16QAM modulation constellation, out of the three bits in each shiftregisters, only two of the three bits are enabled.

Only for 64QAM case, all of the three bits at each register are enabled.

For n-Tx BPSK STTC, the multiplier outputs are added 640 modulo 2; forn-Tx QPSK STTC and n-Tx 16QAM STTC, the multiplier outputs are addedmodulo 4; for n-Tx 64QAM STTC, the multiplier outputs are added modulo8. The output of the adder are then mapped 650 to nBPSK/QPSK/16QAM/64QAM symbols c¹ _(t), . . . , c^(n) _(t). Then, c^(i)_(t) is assigned to the i^(th) (i=1, . . . , n) transmit antenna 651 fortransmission.

We now describe the setup of code generator parameters in the encoder600 for the various modulation constellations.

BPSK STTC

For n-Tx BPSK STTC, the code generator parameters g_(w,i) ¹ (w=0, 1, 2,3; i=1, . . . , n) are the same as those in FIG. 2, and g_(w,i) ² (w=1,2, 3; i=1, . . . , n) are equal to g_(w+3,i) ¹ in FIG. 2. All the othersettings are the same as in FIG. 2.

QPSK STTC

For n-Tx QPSK STTC, all the settings, including the setting of g_(w,i)^(u) (u=1, 2;w=0, 1, . . . , 3; i=1, . . . , n), are the same as in FIG.3.

16QAM STTC

For n-Tx 16QAM STTC, g_(w,i) ^(u) denotes [g_(w,i,I) ^(u), g_(w,i,Q)^(u)]. For g_(w,i) ¹=[g_(w,i,I) ¹, g_(w,i,Q) ¹] (w=0, 1; i=1, . . . ,n), the elements g_(w,i,I) ¹, g_(w,i,Q) ¹ are the same as in FIG. 4. Forg_(w,i) ²=[g_(w,i,I) ², g_(w,i,Q) ²] (w=1, 1, 2; i=1, . . . , n), theelements g_(w,i,I) ², g_(w,i,Q) ² are the same as in FIG. 4. In thiscase, the second and third registers at the upper encoder branch thethird register at the lower encoder branch are not needed; this isimplemented by setting g_(w,i) ¹ (w=2, 3; i=1, . . . , n) and g_(w,i) ²i (w=3; i=1, . . . , n) as [0, 0] for 16QAM case. All the other settingare the same as in FIG. 4.

64QAM STTC

For n-Tx 64QAM STTC, g_(w,i) ^(u) also denotes [g_(w,i,I) ^(u),g_(w,i,Q) ^(u)] For g_(w,i) ^(u)=[g_(w,i,1) ^(u), g_(w,i,Q) ^(u)] (u=1,2; w=0, 1, . . . , n), the elements g_(w,i,I) ^(u), g_(w,i,Q) ^(u) arethe same as in FIG. 5. In this case, the second and third registers ateither the upper or the lower encoder branch are not needed; this isimplemented by setting g_(w,i) ^(u) (u=1, 2; w=2, 3; i=1, . . . , n) as[0, 0] for 64QAM case. All the other setting are the same as in FIG. 5.

Full-Rate Pseudo-STTC for Single-Antenna Transmission

In a single-carrier single-antenna system, for the channel between asingle antenna transmitter and receiver, the instantaneous channelcoefficient at time t (i.e., the channel impulse response) is denoted ash(t). The multipath fading is considered as Rayleigh fading. Then, h(t)can be modeled as a zero-mean complex Gaussian random variable with unitvariance per complex-dimension. The samples of h(t) are independentevery other channel coherence time period.

Within a channel coherence time period, the samples of h(t) are)approximately invariant or they are closely dependent. If the channelcoherence time is large and FEC is used, then a channel interleaver willbe used to increase time diversity achieved by FEC. We assume a flatchannel frequency response and perfect synchronization. At the receiver,the additive noise at time slot t, η(t), is modeled as a zero-meancomplex Gaussian random variable with variance N₀ per complex-dimension.The samples of the noise η(t) are independent for every different t.

FIG. 7 shows a novel full-rate pseudo-STTC scheme for encoding inputbits 701 for single-antenna 702. At each time slot, the single-antennatransmitter multiplies 705 each of n coded MPSK/MQAM output symbols witha complex number ε_(i)(t), and adds 710 the n resulting values togetherto form a linear combination of the output symbols, which are generatedby encoding k=log₂ M information bits using an n-Tx STTC encoder 600.

The data rate of the pseudo-STTC scheme is k bits per channel use. The nlinear coefficients used as the code generating weights for thecombining at time slot t are denoted as ε₁(t), ε₂(t), . . . , ε_(n)(t).At a single-antenna receiver, the received signal at time slot t is

$\begin{matrix}{{{r(t)} = {{{{h(t)}{\sum\limits_{i = 1}^{n}{c_{t}^{i}{ɛ_{i}(t)}}}} + {\eta (t)}} = {{\sum\limits_{i = 1}^{n}{c_{t}^{i}{\alpha_{i}(t)}}} + {\eta (t)}}}},.} & (1)\end{matrix}$

Based on the second equality in Eqn. (1), the pseudo-STTC scheme isequivalent to forming n “virtual antennas.” Here, the equivalentinstantaneous channel coefficient between the virtual antenna i (i=1, .. . , n) and the single-antenna receiver is α_(i)(t)=ε_(i)(t)h(t), andc_(t) ^(i) is transmitted by virtual antenna i. At the receiver, byestimating n equivalent channel coefficients α_(i)(t) (i=1, . . . , n),the pseudo-STTC scheme can use the same coherent decoding algorithm asfor n-Tx STTC with one receive antenna. Similar to conventionalmulti-antenna n-Tx STTC, in the pseudo-STTC scheme for a single antenna,the energy for each of the n coded symbols is E_(c)=kE_(b)/n. After weselect linear coefficients so that |ε_(i)(t)|²=1 for every i ∈ {1, . . ., n}, at each time slot t, the energy of transmitted linearly combinedsignal is ensured to be equal to kE_(b).

For the single-antenna transmitter, transmit diversity gain cannot beachieved by the pseudo-STTC scheme. However, the coding gain can beachieved with full-rate transmissions. In addition, similar toconventional single-antenna FEC techniques, time diversity gain can alsobe achieved for time-varying fading. The order of achieved timediversity gain depends on the channel coherence time. With the channelinterleaver, the time diversity gain can be increased.

Selection of Underlying n-Tx STTC

As we have described, without modifying the detection algorithm, a STTCdesigned for quasi-static flat fading channel can achieve at least thesame end-to-end diversity benefit for other channel conditions. Thus, tomake our pseudo-STTC robust to highly dynamic channel conditionsresulting from non-negligible Doppler spread and delay spread, as wellas imperfect compensation for frequency offset, the underlying n-TxMPSK/MQAM STTC is selected as an n-Tx MPSK/MQAM STTC which iswell-designed for quasi-static flat fading channel.

Linear Coefficient Setting for Full-Rate Pseudo-STTC

The values of linear coefficients ε_(i)(t) (i=1, . . . , n) can berandom or deterministic. For random linear coefficients, theuniform-phase randomization is a good choice. In this case,ε_(i)(t)=e^(jθ) ^(i) and θ_(i) (i=1, . . . , n) are uniformlydistributed over [0, 2π]. When ε_(i)(t) (i=1, . . . , n) are set asrandom values, to decide how fast they change to use newly generatedindependent samples, let us first consider the following facts: (a) whenthe pseudo-STTC scheme is employed at the receiver, the channelestimation needs to be done by estimating the equivalent channelcoefficients α_(i)(t)=ε_(i)(t)h(t) (i=1, . . . , n); (b) the originalchannel h(t) has independent variation every other channel coherencetime period, more quick variation of ε_(i)(t) (i=1, . . . , n) would notbring additional performance benefit; (c) generally, the channelestimation is performed by periodically inserting a bunch of pilotsymbols into the transmitted data, and the insertion period is roughlyset to the predicted value of channel coherence time.

Based on the above observations, to avoid increasing the burden ofchannel estimation without benefit, the random linear coefficients donot need to change every time slot; the coefficients can be set to usenew samples only when a new bunch of pilot symbols are inserted. Bydoing so, roughly, the random linear coefficients change every otherchannel coherence time period.

If the n linear coefficients are set as deterministic values, then weeven do not need to estimate the n equivalent channel coefficients,because α_(i)(t)=ε_(i)(t)h(t) can be obtained by multiplying theestimated h(t) with the fixed values of ε_(i)(t)=ε_(i) (i=1, . . . , n).This is a big advantage because we do not need to do any modificationfor channel estimation processing. However, most deterministic linearcoefficients result in worse error performance when compared withuniform-phase randomized linear coefficients. Thus, it is significant todesign n deterministic linear coefficients that can provide similar orbetter error performance than using random coefficients, such as theuniform-phase randomization.

Optimization on Deterministic Linear Coefficients for Full-RatePseudo-STTC

By realizing (a) if the number of antennas for multi-antenna WAVEtransceivers is n, the underlying code used by the single-antennapseudo-STTC can be selected as n-Tx STTC, and (b) in the recent future,the multi-antenna WAVE devices would probably employ two antennas, inthis embodiment of the invention, when we consider the specificpseudo-STTC scheme, the underlying STTC is chosen as 2-Tx STTC.

We optimize the deterministic linear coefficients for the pseudo-STTCusing 2-Tx STTC as the underlying code. The general expressions for n=2deterministic linear coefficients is ε₁(t)=ε₁=e^(j0) ¹ andε₂(t)=ε₂=e^(jθ) ² , where θ₁ and θ₂ are two fixed phases. Based onanalyzing the upper bound on pair-wise error probability (PEP), it isfound that, if we want can use the derived upper bound on PEP, we canspecify the underlying code as a 2-Tx STTC with a given modulationconstellation.

We focus on the case using a 2-Tx QPSK STTC as the underlying code.Then, by utilizing the derived upper bound on the pair-wise errorprobability (PEP), we obtain the following results: if |θ₁−θ₂|=π, themaximum of PEP upper bound is minimized. However, this choice ofdeterministic linear coefficients still result in worse errorperformance than the uniform-phase randomized case. This is because thederived PEP upper bound is not that tight enough for effectiveoptimization.

We believe that the optimal |θ₁−θ₂ is equal to π±ξ, where ξ is a smallpositive number. When verifying this conjecture via numericalsimulations, we choose the underlying code as a “good” 2-Tx QPSK64-state STTC designed for quasi-static flat fading channel, which hasthe same number of trellis states as the convolutional code used in802.11p.

It is verified by simulations that, if two fixed phases θ₁ and θ₂ cansatisfy |θ₁−θ₂|=4π/5, for the focused pseudo-STTC scheme, thedeterministic linear coefficients ε₁(t)=ε₁=e^(jθ) ¹ and ε₂(t)=ε₂=e^(jθ)² results in better error performance than the uniform-phase randomizedcase. The can exist another “good” choices for θ_(i) (i=1, 2), and theobtained optimized result is empirical. However, the theoretic analysisstill give us a helpful indication. Actually, the indication about|θ₁−θ₂|_(opt)=π±ξ helps us to avoid using exhaustive simulations toinvestigate the effect on error performance for infinite possibleparticular values of θ₁ and θ₂.

Unified Codec Module for Single- And Multi-Antenna Transceivers

For future WAVE transceivers equipped with n (n≧2) antennas, we have useSTTC as the MIMO coding scheme. In order to unify the codec module usedfor single-antenna full-rate pseudo-STTC and conventional n-Tx STTC,each antenna of the n-Tx transmitter performs the same operation as thesingle-antenna transmitter employing the full-rate pseudo-STTC. That is,each of the n transmit antennas also sends a linear combination of ncoded symbols generated by n-Tx STTC encoder. For this kind ofmulti-antenna coded transmission to be equivalent to conventional n-TxSTTC, we set the values of n linear coefficients to be some specialfixed numbers. Specifically, for antenna i (i=1, . . . , n), the valuesof the linear coefficients are set as ε_(i)(t)=1 and ε_(j)(t)=0 for j≠i.By doing so, at each time slot t, c_(t) ^(i) is transmitted by antenna i(i=1, . . . , n), resulting in conventional n-Tx STTC transmissions.

Duplicated Pseudo-STTC for Single-Antenna Transmission

According to the IEEE 802.11p standard, the convolutional code with coderate of R_(c)=½ can be punctured to achieve a higher code rate, e.g.,R_(c)=¾, although with a worse error performance. To provide flexiblecode rate and better error performance, we to perform “duplication” onthe full-rate pseudo-STTC.

As shown in FIG. 8, the n-Tx STTC encoder 600 encodes k=log₂ Minformation bits 801 into n coded MPSK/MQAM symbols. For every n codedsymbols, the single-antenna transmitter sends q (q≧2) different versionsof the linear combination 810 of these n coded symbols. The data rate ofthis duplicated scheme is k/q bits per channel.

For the full-rate pseudo-STTC, every linearly combined transmissioncorresponds to a unique time slot in the trellis. Thus, the time slotindex for transmissions is the same as that for the trellis. However,for the q-duplicated pseudo-STTC, every q (q≧2) linearly combinedtransmissions correspond to a unique time slot in the trellis, so thatthe time slot index for transmissions is different from that for thetrellis.

For the q-duplicated pseudo-STTC, we use t to denote the index of“trellis time slot”, and we use t′ to denote the index of “transmissiontime slot,” If we let the starting time slot in the trellis be t=1 foreach codeword, and let the starting time slot for transmitting acodeword (using the q-duplicated pseudo-STTC) be always normalized ast′=1, each trellis time slot corresponds to q transmission time slots,with the relationship of t₁′=q(t−1)+1, . . . , t′=q(t−1)+q=q×t.

Then, for n coded symbols c_(t) ¹, . . . , c_(t) ^(n) generated attrellis time slot t, the corresponding q sets of linear coefficientsthat are used for q different versions of linearly combined signals aredenoted as ε_(1j)(t), ε_(2j)(t), . . . , ε_(nj)(t) (j=1, . . . , q), andthe instantaneous channel coefficients during the transmissions of qlinearly combined signals are h(t′_(j)) (j=1, . . . , q). Accordingly,the q received signals at the single-antenna receiver are

$\begin{matrix}{{{r\left( t_{j}^{\prime} \right)} = {{{{h\left( t_{j}^{\prime} \right)}{\sum\limits_{i = 1}^{n}{c_{t}^{i}{ɛ_{ij}(t)}}}} + {\eta \left( t_{j}^{\prime} \right)}} = {{\sum\limits_{i = 1}^{n}{c_{t}^{i}{\alpha_{ij}(t)}}} + {\eta \left( t_{j}^{\prime} \right)}}}},{j = 1},\ldots \mspace{14mu},{q.}} & (2)\end{matrix}$

Based on the second equality in Eqn. (2), the q-duplicated pseudo-STTCscheme is equivalent to letting the i^(th) “virtual antenna” perform qrepeated transmissions of c_(t) ^(i), (i=1, . . . , n). Between thei^(th) virtual antennas and the receiver, the equivalent instantaneouschannel coefficients for q repeated transmissions areα_(ij)(t)=ε_(ij)(t)h(t′_(j)) (j=1, . . . , q). Compared with Viterbidecoding for the full-rate pseudo-STTC, the decoder of q-duplicatedpseudo-STTC only modifies the branch metric.

In particular, the branch metric is the sum of q values, each of whichis obtained by using one of the q received signals r(t′_(j)) (j=1, . . ., q) to do the same calculation of branch metric as for the full-ratepseudo-STTC.

For the q-duplicated pseudo-STTC scheme, the energy for each of the ncoded symbols is E_(c)=kE_(b)/n. After we select linear coefficients sothat |ε_(ij)(t)|²=1/q for every i ∈ {1, . . . , n} and every j ∈ {1, . .. , q}, the total transmit energy of q duplicated linearly combinedsignals is ensured to be kE_(b). That is to say, when all the q×n linearcoefficients are non-zero, an inherent power normalization factor1/√{square root over (q)} can be included by each linear coefficient,regardless of the following description about setting appropriate valuesfor linear coefficients to achieve good error performance.

Linear Coefficient Setting for Duplicated Pseudo-STTC

As for the full-rate pseudo-STTC, the values of linear coefficientsε_(ij)(t) (i=1, . . . , n; j=1, . . . , q) can be either random ordeterministic. Using uniform-phase randomized linear coefficients isalso a good choice for the q-duplicated pseudo-STTC. It is significantto design q×n deterministic linear coefficients that can provide similaror better error performance than using the uniform-phase randomizedcoefficients.

For the q-duplicated pseudo-STTC using n-Tx STTC as the underlying code,if we select q=n, and set the values of q×n=n² linear coefficientcoefficients as ε_(ij)(t)=ε_(ij)=1 for i=j and ε_(ij)(t)=ε_(ij)=0 fori≠j (i=1, . . . , n; j=1, . . . , n), we obtain a special transmissionscheme. In this scheme, the single-antenna transmitter separately sendseach of n coded symbols c_(t) ¹, . . . , c_(t) ^(n), which are generatedat trellis time slot t, over each of n transmission time slots t₁′, . .. , t_(n)′.

Optimization on Deterministic Linear Coefficients for DuplicatedPseudo-STTC

In the IEEE 802.11p standard, the specified modulation constellationsinclude BPSK, QPSK, 16QAM, and 64QAM. Because, regardless of the usedmodulation constellation, the 2-duplicated pseudo-STTC achieves the samedata rate as employing the convolutional code used in IEEE 802.11p. Weoptimize deterministic linear coefficients by focusing on 2-duplicatedpseudo-STTC. In addition, as described before, in this invention, wefocus on the case of using 2-Tx STTC as the underlying code.

For the 2-duplicated pseudo-STTC, which uses 2-Tx STTC as the underlyingcode, q×n=2×2=4 deterministic linear coefficients can be expressed asq=2 deterministic coefficient vectors ε₁=[ε₁₁, ε₂₁]^(T) and ε₂=[ε₁₂,ε₂₂]^(T). For every q=2 duplicated transmissions, the i^(th) (i=1, 2)duplicated linearly combined signal uses ε_(i). Based on analyzing theupper bound on PEP, if ε₁ and ε₂ are two orthogonal vectors withε_(ij)≠0 (i=1, 2; j=1, 2), the maximum of PEP upper bound can beminimized. Verified by numerical simulations, this optimizeddeterministic linear coefficients can provide better error performancethan the uniform-phase randomized case.

Unified Codec Module: Apply Duplication to n-Tx STTC Transmission

The duplication concept can also be used by conventional full-rate n-TxSTTC (n≧2) to achieve lower rate and larger redundancy. Formulti-antenna transceivers employing n-Tx STTC, a straightforwardduplication operation is to let the i^(th) antenna perform q repeatedtransmissions for c_(t) ^(i) (i=1, . . . , n). In this way, while thedata rate becomes lower, additional time diversity gain can be achieveddepending on channel coherence time, codeword length, and channelinterleaver depth.

To unify the codec module used for both n-Tx q-duplicated STTC andsingle-antenna q-duplicated pseudo-STTC, let each antenna element of then-Tx transmitter also send q linear combinations of c_(t) ¹, . . . ,c_(t) ^(n). This is equivalent to n-Tx q-duplicated STTC when, forantenna i (i=1, . . . , n), the linear coefficients used for each of qlinearly combined transmissions are the same and have the format ofsetting the linear coefficient multiplied with c_(t) ^(i) as 1 and allthe others as 0.

Apply Proposed Coding Schemes to OFDM-Based Single-Antenna Network

We describe our coding techniques in the context of an OFDM-basedsingle-antenna network, such as WAVE network. We consider asingle-antenna OFDM network with L subcarriers (e.g., L=52 in 802.11p).Among L subcarriers in one OFDM symbol, only L_(CD) (L_(CD)<L)subcarriers are used to for coded data signals (e.g., L_(CD)=48 in802.11p). If a packet is composed of V (V≧1) consecutive OFDM symbols,then one packet can totally load V×L_(CD) coded data signals. When ourcoding technique is used as the FEC scheme, these coded data signals areobtained from encoding the data bits via employing the full-rate orq-duplicated pseudo-STTC, followed by interleaving. While the channelimpulse response of the fading channel can vary within the duration of apacket, it is assumed to be effectively invariant within the duration ofeach OFDM symbol. Further, it is assumed that the maximum delay spreadof the channel is smaller than the length of cyclic prefix (CP) andsynchronization is perfectly done.

FIG. 9 shows stages at a PHY layer in a single-antenna OFDM networkusing our pseudo-STTC. At a transmitter, input bits 901 are input to ourpseudo-STTC encoder 910, and encoded symbols are interleaved 920. Pilotsymbols are inserted 930 and applied to an inverse fast Fouriertransform (IFFT) 950 and passed through a channel 960. Before performingIFFT, within each packet, denote C[v, l] as the coded data signalassigned to subcarrier l (l=1, . . . , L) at the v-th (v=1, . . . , V)OFDM symbol in this packet. At the receiver, after performing FFT, thecorresponding received version of C[v, l] can be expressed as

R[v,l]=H[v,l]C[v, l]+Z[v,l],   (3)

In Eqn. (3), H[v, l] denotes the channel frequency response coefficientsover subcarrier l (l=1, . . . , L) at the v-th (v=1, . . . , V) OFDMsymbol in the considered packet, and Z[v, l] is zero-mean additive whiteGaussian noise. For any given v, H[v, l₁] and H[v, l₂] (l₁≠l₂) areindependent in ideal case; in practice, they can be correlated to acertain extent.

At a receiver, the CP is removed 970, and a FFT 980 is applied. Thepilot symbols are removed 990, de-interleaved 995 and decoded 996 toobtain decisions 902.

When the q-duplicated pseudo-STTC is used, in order to achieve themaximum possible time diversity benefit provided by this coding scheme,it is required for every q duplicated coded signals to be assigned to qdifferent subcarriers. In practical applications, q is a small valuesuch as q=2; thus, it is easy to implement this kind of subcarrierallocation.

Although the invention has been described with reference to certainpreferred embodiments, it is to be understood that various otheradaptations and modifications can be made within the spirit and scope ofthe invention. Therefore, it is the object of the append claims to coverall such variations and modifications as come within the true spirit andscope of the invention.

1. An apparatus for encoding an input bitstream in a transmitter usingspace-time trellis coding (STTC), comprising: encoding the inputbitstream to produce in parallel a set of output symbols; a multiplierto multiply each output symbols with complex number; an adder to sum upall multiplied values to form a linear combination of the outputsymbols.
 2. The apparatus of claim 1, wherein the complex number takesthe form e^(jθ), where e is the natural number, j=√{square root over(−1)} is an imagine number, and θ is chosen by the transmitter, andtakes on a value between −π and π.
 3. The apparatus of claim 2, whereinthe value θ is drawn from a uniform distribution in the range −π and π.4. The apparatus of claim 2, wherein in the case of quadraturephase-shift keying (QPSK) using a two transmit antenna (2-Tx) STTCencoder, there are two complex numbers, e^(jθ1) and e^(jθ2), andmultiplying the output symbols have the relationship |θ₁−θ₂|=4π/5. 5.The apparatus of claim 1, wherein each set of output symbols ismultiplied by a plurality of complex vectors to form a plurality oflinear combinations.
 6. The apparatus of claim 5, wherein the complexvectors are orthogonal.
 7. The apparatus of claim 5, wherein each valuein the complex vectors take a form e^(jθ), and a value θ is drawn from auniform distribution in a range −π and π.